No, it isn't like the app you used pre-root. Generally when a custom ROM is talking about a2sd is means redirecting the /data/app directory from internal memory to an ext format partition which has been added to the SD card. In most cases you don't need to do anything to use it apart from partition the card and flash the ROM, though some a2sd scripts do need a little setting up by the user to get the full benefit. It has the advantage that it works even for apps with widgets, which don't work if moved to the SD card google-style.
I'm guessing that you should use the other version of that ROM, because you don't have the CM7 partition table. But as I say, I don't know the details of that ROM, and they don't make it terribly clear in their descriptions exactly how the 2 versions differ. However, there's no way that ROM is going to fit in system storage with the CM7 partition, which is much smaller than with the default table (130MB rather than 250MB), so the CM7 version must be putting a lot of the ROM in the ext partition, and presumably then using internal for user apps. That would be OK if you had the CM7 memory table, because that would give you more internal space, but not ideal with the default setup. You could check by installing an app called Quick System Info and then seeing what it says about your Internal, System and A2SD storage (how much space and how much is free in each).
If I'm right, you could in principle solve it by changing to the CM7 table. But that's not something you should rush straight into - you should make sure you know what you are doing first. So it would probably be better to use the a2sd version of the ROM for now. Take a nandroid backup first, so that you can get back to where you are now should there be any problem.
But if you do run Quick System Info first, I'd be interested in what it says, just to know whether I've guessed right what this ROM is doing. If it's intended for the CM7 table it should report that you have at least 120MB free in System storage (out of 250 total), and presumably be using a bit more than 120MB of "a2sd storage".
If you want to know what these tables I talk about are, read the alpharev website fully
